In a scientific workflow system, a checkpoint selection strategy is used to select checkpoints along scientific workflow execution for verifying temporal constraints so that we can identify any temporal violations and handle them in time in order to ensure overall temporal correctness of the execution that is often essential for the usefulness of execution results. The problem of existing representative strategies is that they do not differentiate temporal constraints as, once a checkpoint is selected, they verify all temporal constraints. However, such a checkpoint does not need to be taken for those constraints whose consistency can be deduced from others. The corresponding verification of such constraints is consequently unnecessary and can severely impact overall temporal verification efficiency while the efficiency determines whether temporal violations can be identified quickly for handling in time. To address the problem, in this article, we develop a new temporal-dependency based checkpoint selection strategy which can select checkpoints in accordance with different temporal constraints. With our strategy, the corresponding unnecessary verification can be avoided. The comparison and experimental simulation further demonstrate that our new strategy can improve the efficiency of overall temporal verification significantly over the existing representative strategies.